Goldstone Inflation

TL;DR

This work proposes a sub-Planckian, radiatively stable inflaton realized as a pseudo-Goldstone boson from a global G→H breaking pattern, with the Coleman–Weinberg potential generated by gauge and fermion loops in an SO(N) strong sector. The leading single-field potential takes the form V(φ) = Λ^4 [C_Λ + α cos(φ/f) + β sin^2(φ/f)], with α ≈ 2β, enabling a flat enough region for inflation even when f < M_p. The analysis connects inflationary observables to the UV structure via form-factor relations, examines non-Gaussianity and the speed of sound through Goldstone scattering constraints, and discusses a light-resonance UV completion that can yield the required α–β relation; it also shows how hybrid inflation can be accommodated within the same Goldstone framework. The model predicts negligible tensors for sub-Planckian f and yields testable links between the IR inflationary dynamics and the UV spectrum, offering a constrained, predictive path for Goldstone-driven inflation and reheating dynamics.

Abstract

Identifying the inflaton with a pseudo-Goldstone boson explains the flatness of its potential. Successful Goldstone Inflation should also be robust against UV corrections, such as from quantum gravity: in the language of the effective field theory this implies that all scales are sub-Planckian. In this paper we present scenarios which realise both requirements by examining the structure of Goldstone potentials arising from Coleman-Weinberg contributions. We focus on single-field models, for which we notice that both bosonic and fermionic contributions are required and that spinorial fermion representations can generate the right potential shape. We then evaluate the constraints on non-Gaussianity from higher-derivative interactions, finding that axiomatic constraints on Goldstone boson scattering prevail over the current CMB measurements. The fit to CMB data can be connected to the UV completions for Goldstone Inflation, finding relations in the spectrum of new resonances. Finally, we show how hybrid inflation can be realised in the same context, where both the inflaton and the waterfall fields share a common origin as Goldstones.

Figures (6)

• Figure 1: Subgroups of the global $SO(N)$ symmetry.
• Figure 2: Form of the potential: Shape of the potential for $\tilde{\beta} = \pm 1/2$ respectively. Different values will interpolate between these extreme cases. We show the shape of the vanilla NI \ref{['vanilla']} for comparison. The height of the potential is normalised to $\Lambda$.
• Figure 3: Model predictions: Parameters $n_s$ and $r$ plotted against the Planck 2015 data Planck2015 for the model \ref{['model']} for $f = M_p$ (red upper bound). For lower values $f < M_p$, $r \rightarrow 0$ (shaded region).
• Figure 4: Tuning: The parameter $\Delta$ as defined above for $V = \Lambda^4 \left(C_\Lambda + \alpha \cos\phi/f+ \beta \sin^2 \phi/f\right)$. Outside of the pink zone the spectral index $n_s$ predicted by the model is incompatible with the Planck data ($n_s < .948$ above the region, $n_s > .982$ below).
• Figure 5: Sound speed: Predictions for $c_2 \, x$. In dark grey the Planck bound; the shaded region indicates the perturbativity bound. The continuous lines are the predictions for $c_2 >0$, which is relevant for our model as discussed in the text. We also indicate the hypothetical situation $c_2 < 0$ with dashed curves. It is seen that the prediction approaches the asymptote $c_s = 1 / \sqrt{3}$ for large $c_2$, as expected from \ref{['soundspeedmodel']}.